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A Banach space is a complete normed vector space: A vector space equipped with a norm such that every Cauchy sequence converges.

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Classification of subsymmetric basic sequences

A more detailed version of the above proof: Assume that $(x_n)$ is not weakly null. Then, passing to a subsequence, we get a functional $x^*$ such that $\inf_n |x^*(x_n)|>0$. By unconditionality, ther …
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Maurey-Pisier Theorem for complex Banach spaces

A famous theorem of Maurey and Pisier, usually stated for real Banach spaces, says that $\ell_a$ and $\ell_b$ are finitely representable in $X$, where $a$ is the supremum of the $p$ such that $X$ has …
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